Applications of the general root-locus theory for nonlinear systems

摘要

The general root locus theory is a theory of designing, analysisand synthesis of root hodographs in arbitrary variation laws of anypreset parameters of automatic control systems and their combinations.On this basis it is considered an analysis of absolute stability,hyperstability, L-stability of nonlinear control systems. A roothodograph of conical sections is used, under which we name the mappingof curve of the second order of complex plane W=G(p), W-u+iv onto acomplex plane p-+i, realized by means of a function inverse to thefunction of the linear part of the system. Root conditions require thatfor a system to be absolutely stable it is necessary that all thebranches of at least one root hodograph of conical images are locatedcompletely on the left semiplane of plane p